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arXiv · 1607.05547

Fast Algorithms for Diameter-Optimally Augmenting Paths and Trees

Ulrike Große·Joachim Gudmundsson·Christian Knauer·Michiel Smid·Fabian Stehn
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Abstract

We consider the problem of augmenting an n-vertex graph embedded in a metric space, by inserting one additional edge in order to minimize the diameter of the resulting graph. We present exact algorithms for the cases when (i) the input graph is a path, running in O(n \log^3 n) time, and (ii) the input graph is a tree, running in O(n^2 \log n) time. We also present an algorithm that computes a (1+\eps)-approximation in O(n + 1/\eps^3) time, for paths in R^d, where d is a constant.

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Ulrike Große, Joachim Gudmundsson, Christian Knauer, Michiel Smid, Fabian Stehn. 2016-07-19. Fast Algorithms for Diameter-Optimally Augmenting Paths and Trees. https://arxiv.org/abs/1607.05547

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